Reading Question and the excercise - C31

What is the easiest way to recognize if a square matrix is nonsingular or not?

The easiest way to determine a square matrix is non-singular if the determinent of matrix is non zero. when a square matrix A is called non-singular, only if there is an inverse exist(i.e A−1)

A_Inverse = 1/det(A) * Adj(A)

if det(A) is zero, A_inverse doesnt exist, there by matrix A is a singular.

if det(A) is non-zero, A_inverse do exist, there by matrix A is non-singular.

note: What if the matrix is rectangular matrix(m ≠ n ). In this case, there is no inverse exist. So a rectangular matrix can not be a singular or non-singular.

C30 excercise Determine if the matrix is nonsingular or singular. Give reasons for your answer.

Since the determinent of A is non zero, the given matrix is a non singular.

matrix_elements = c(3,2,1,5,1,0,2,1,2,3,7,2,8,4,4,0)
MatrixA = matrix(matrix_elements,nrow=4, ncol=4)
print(MatrixA)
##      [,1] [,2] [,3] [,4]
## [1,]    3    1    2    8
## [2,]    2    0    3    4
## [3,]    1    2    7    4
## [4,]    5    1    2    0
det(MatrixA)
## [1] 264

C31 excercise Determine if the matrix is nonsingular or singular. Give reasons for your answer.

Since the determinent of A is 0, the given matrix is a singular( or non-invertible)

matrix_elements = c(2,1,-1,1,3,1,2,2,1,1,3,1,4,0,5,3)
MatrixA = matrix(matrix_elements,nrow=4, ncol=4)
print(MatrixA)
##      [,1] [,2] [,3] [,4]
## [1,]    2    3    1    4
## [2,]    1    1    1    0
## [3,]   -1    2    3    5
## [4,]    1    2    1    3
det(MatrixA)
## [1] 0